In this video, I present one of the most influential formulations of classical physics — Hamiltonian mechanics. This is a walk through the birth of Hamiltonian mechanics and how Hamilton extended Lagrange’s work into a new, elegant formulation that would go on to influence quantum theory, statistical mechanics, and dynamical systems.

In this video, I present an overview of symmetries in physics, passive vs. active transformations, and how to derive Noether’s theorem from the Euler-Lagrange equations. Different examples are presented in detail to show how the invariance under specific symmetries can be used to construct conserved quantities.

A brief history and derivation of Lagrangian mechanics from Newtonian mechanics.